Let $f$ be a function such that $f(x) + 3f\left(\frac{24}{x}\right) = 4x$,where $x \neq 0$. Then $f(3) + f(8)$ is equal to:

If $f(x)$ is a function satisfying the condition $f(x) = \frac{1}{3}\left[ f(x + 6) + \frac{6}{f(x + 7)} \right]$ and $f(x) \geq 0$ for all $x \in R$. If $\lim_{x \to \infty} f(x) = \sqrt{m}$,then the value of $m$ is:

Let $f$ be a differentiable function satisfying the relation $f(xy) = xf(y) + yf(x) - 2xy$ for all $x, y > 0$ and $f'(1) = 3$. Which of the following statements is true?

If $f(x)$ is a function such that $f(x+y)=f(x)+f(y)$ and $f(1)=7$, then $\sum_{r=1}^n f(r)=$

Let $R$ be the set of all real numbers. The number of continuous functions $f: R \rightarrow R$ such that for all real $x$,$f(x) + f(2x) = 0$ is

If $f(0)=0, f(1)=1, f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3, 4, 5, \ldots$,then $f(9)$ is equal to